Department of Mathematics and Statistics

Department of Mathematics and Statistics
Department of Mathematics and Statistics
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Free Probability and Random Matrices Seminar

Probability Seminar - Pei-Lun Tseng (Queen’s University)

Tuesday, March 10th, 2020

Time: 1:30-2:30 p.m.  Place: Jeffery Hall 422

Speaker: Pei-Lun Tseng (Queen’s University)

Title: Infinitesimal Central Limit Theorem.

Abstract:  In this talk, we will review the four notions of infinitesimal independence, and derive associated central limit theorems.

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Probability Seminar - Daniel Perales Anaya (Waterloo)

Tuesday, March 3rd, 2020

Time: 1:30-2:30 p.m.  Place: Jeffery Hall 422

Speaker: Daniel Perales Anaya (Waterloo)

Title: Relations between infinitesimal non-commutative cumulants.

Abstract:  Boolean, free and monotone cumulants as well as relations among them, have proven to be important in the study of non-commutative probability theory (e.g, using Boolean cumulants to study free infinite divisibility via the Boolean Bercovici-Pata bijection). On the other hand, we have the concept of infinitesimally free cumulants (and the analogue concept for Boolean and monotone under the name of cumulants for differential independence).

In this talk we first are going to discuss the basic properties of non-commutative infinitesimal cumulants. Then we will use the Grassmann algebra to show that the known relations among free, Boolean and monotone cumulants still hold in the infinitesimal framework. Later we will review how the relations between the various types of cumulants are captured via the shuffle algebra approach to moment-cumulant relations in non-commutative probability theory. Finally, we will observe how the shuffle algebra approach naturally extends to the notion of infinitesimal non-commutative probability space, and we will present some interesting formulas in this setting. This is a joint work with Adrian Celestino and Kurusch Ebrahimi-Fard.

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Probability Seminar - Jamie Mingo (Queen's University)

Tuesday, February 25th, 2020

Time: 1:30-2:30 p.m.  Place: Jeffery Hall 422

Speaker: Jamie Mingo (Queen's University)

Title: Free Compression of Bernoulli Random Variables.

Abstract:  If we represent a Bernoulli random variable by a diagonal matrix with ± 1 entries (half 1, half -1) and then randomly rotate it with an orthogonal matrix, we can then cut out the matrix in the upper left hand corner, of arbitrary size. This is the free compression of an Bernoulli random variable (approximately). This compression has the distribution of the sum of several free Bernoulli random variables, including fractionally many. We will relate this to the Kesten-McKay law for random regular graphs.

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Probability Seminar - Jamie Mingo (Queen's University)

Tuesday, February 11th, 2020

Time: 1:00-2:00 p.m.  Place: Jeffery Hall 202

Speaker: Jamie Mingo (Queen's University)

Title: A Survey of the Weingarten Calculus.

Abstract:  The Weingarten calculus is a method for calculating the expectation of products of entries of Haar distributed unitary (or orthogonal) matrices. The basic tool is Schur-Weyl duality, however I will present an approach based on Jucys-Murphy operators. The Weingarten calculus started with Don Weingarten in 1978. Many authors have contributed since then. This talk will be based on papers of Collins, Sniady, and Zinn-Justin.

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Probability Seminar - Sang-Gyun Youn (Queen's University)

Wednesday, May 1st, 2019

Time: 3:30-5:00 p.m.  Place: Jeffery Hall 319

Speaker: Sang-Gyun Youn (Queen's University)

Title: Minimum output entropy and capacities of quantum channels.

Abstract:  In this talk, minimum output entropy (MOE) and Holevo/quantum capacity of quantum channels will be discussed. And I will sketch how the additivity conjecture of MOE was disproved by random unitary channels.

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Probability Seminar - Jamie Mingo (Queen's University)

Monday, January 21st, 2019

Time: 10:00-11:30 a.m.  Place: Jeffery Hall 319

Speaker: Jamie Mingo (Queen's University)

Title: Tensor Products of Modules and Vector Spaces.

Abstract:  This talk will review the construction of the tensor product of modules and its universal property. This property can be used to establish associativity, commutativity over direct sums, and a check for linear independence when our modules are vector spaces. I also hope to give a brief introduction to tensor norms.

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Probability Seminar - Sang-Gyun Youn (Queen's University)

Thursday, November 29th, 2018

Time: 4:30-6:00 p.m.  Place: Jeffery Hall 422

Speaker: Sang-Gyun Youn (Queen's University)

Title: Some questions on Jones-Wenzl projections in view of quantum information theory.

Abstract:  It is very natural to study separability or PPT property of quantum states in view of quantum information theory and the need to study those properties for so-called Jones-Wenzl projections has emerged in recent years. In this talk, I am going to introduce the notions of separability, PPT property and Jones-Wenzl projections.

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